Morphological Area Openings and Closings for Grey-scale Images

  • Luc Vincent
Part of the NATO ASI Series book series (volume 126)


The filter that removes from a binary image the components with area smaller than a parameter λ is called area opening. Together with its dual, the area closing, it is first extended to grey-scale images. It is then proved to be equivalent to a maximum of morphological openings with all the connected structuring elements of area greater than or equal to λ. The study of the relationships between these filters and image extrema leads to a very efficient area opening/closing algorithm. Grey-scale area openings and closings can be seen as transformations with a structuring element which locally adapts its shape to the image structures, and therefore have very nice filtering capabilities. Their effect is compared to that of more standard morphological filters. Some applications in image segmentation and hierarchical decomposition are also briefly described.


area opening extrema filtering opening and closing mathematical morphology shape. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cheng, F., Venetsanopoulos, A.N. (1991). Fast, adaptive morphological decomposition for image compression, Proc. 25th Annual Conf. on Information Sciences and Systems, pp. 35–40.Google Scholar
  2. 2.
    Grimaud, M. (1992). A new measure of contrast: dynamics, Proc. SPIE Vol. 1769, Image Algebra and Morphological Processing III, San Diego CA.Google Scholar
  3. 3.
    Knuth, D.E. (1973). The Art of Computer Programming, Vol. 3: Sorting and Searching, Addison Wesley.Google Scholar
  4. 4.
    Lantuéjoul, Ch., Maisonneuve, F. (1984) Geodesic methods in image analysis, Pattern Recognition 17, pp. 117–187.CrossRefGoogle Scholar
  5. 5.
    Laÿ, B. (1987). Recursive Algorithms in Mathematical Morphology, Acta Stereo-logica, Vol. 6/III, Proc. 7th Int. Congress For Stereology, pp. 691–696.Google Scholar
  6. 6.
    Maragos. P., Schafer, R.W. (1987). Morphological filters—part II: their relations to median, order-statistics, and stack filters, IEEE Trans. on Acoustics, Speech, and Signal Processing 35 (8), pp. 1170–1184.MathSciNetCrossRefGoogle Scholar
  7. 7.
    Matheron, G. (1975). Random Sets and Integral Geometry, J. Wiley and Sons, New York.Google Scholar
  8. 8.
    Meyer, F. (1979). Iterative image transformations for the automatic screening of cervical smears, J. Histochem. and Cytochem. 27, pp. 128–135.CrossRefGoogle Scholar
  9. 9.
    Meyer, F. (1990). Algorithme ordonné de ligne de partage des eaux, Tech. Report CMM, School of Mines, Paris.Google Scholar
  10. 10.
    Serra, J. (1982). Image Analysis and Mathematical Morphology, Academic Press, London.zbMATHGoogle Scholar
  11. 11.
    Serra, J. (ed.) (1988). Image Analysis and Mathematical Morphology, Part II: Theoretical Advances, Academic Press, London.Google Scholar
  12. 12.
    Serra, J., Vincent, L. (1992). An overview of morphological filtering, Circuits, Systems, and Signal Processing 11 (1), pp. 47–108.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Soille, P., Serra, J., Rivest, J-F. (1992). Dimensional measurements and operators in mathematical morphology, Proc. SPIE Vol. 1658 Nonlinear Image Processing III, pp. 127–138.Google Scholar
  14. 14.
    Sternberg, S.R. (1986). Grayscale morphology, Computer Vision, Graphics, and Image Processing 35, pp. 333–355.CrossRefGoogle Scholar
  15. 15.
    Vincent, L. (1990). Algorithmes Morphologiques à Base de Files d’Attente et de Lacets. Extension aux Graphes, PhD dissertation, School of Mines, Paris.Google Scholar
  16. 16.
    Vincent, L. (1992). Morphological grayscale reconstruction; definition, efficient algorithm, and applications in image analysis, Proc. IEEE Conf. on Computer Vision and Pattern Recognition, Champaign IL, pp. 633–635.Google Scholar
  17. 17.
    Vincent, L. (1993). Morphological grayscale reconstruction in image analysis: applications and efficient algorithms, IEEE Trans. on Image Processing, 2, pp. 176–201.CrossRefGoogle Scholar
  18. 18.
    Vincent, L. (1992). Morphological algorithms. In: Dougherty, E. (ed.), Mathematical Morphology in Image Processing, Marcel-Dekker, New York.Google Scholar
  19. 19.
    Wendt, P.D., Coyle, E.J., Gallagher, N.C. (1986). Stack filters, IEEE Trans. on Acoustics Speech, and Signal Processing 34 (4), pp. 898–911.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Luc Vincent
    • 1
  1. 1.Xerox Imaging SystemsPeabodyUSA

Personalised recommendations